Young symmetrizer

Named after British mathematician Alfred Young.

Young symmetrizer (plural Young symmetrizers)

1. (mathematics) An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space ${\displaystyle V^{\otimes n}}$ obtained from the action of ${\displaystyle S_{n}}$ on ${\displaystyle V^{\otimes n}}$ by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers.